In this article you can read some rose protection recommendations from an Alberta source where they have rather more severe winters, and wildly fluctuating spring temperatures that can be as damaging as the absolute cold, than in much of Canada and certainly colder than your specified zone.
Since many roses are grafted, the first thing to check is that your wonderful new shoots actually come from the top part of the rose and not the root. If these shoots are root suckers then this would explain their vigour, but might not be worth saving particularly if you put a lot of work into protection. This is where a picture of your plant actually comes in very handy, readers can see what the situation is and adjust their suggestions.
If the shoots are truly from the good top part of the rose then building protection to four feet will require some work. You might be looking at a compromise to save a few feet less for greater manageability when building a protective structure and filling with dead leaves and finally covering with snow. Resist the temptation to uncover too early in the spring, late frosts can be a real surprise.